Compositing fog destroys PNG alpha in Images as Planes when using Cycles
The problem is Z Channel in Cycles - it does not take into account material transparency:



I recommend not using the Z channel pass but to render nice custom Z pass like this:

Assign this material to scene objects (this material has value based of ray length - distance to camera):





You will get nice anti-aliased Z-depth render that you can use for the mist.  For alpha-transparent planes mix in Transparent shader like in the image and render them on separate render layer so there's nothing behind them (then composite them back in).

To create group node group them with Ctrl+G. Go inside and outside group node with Tab.